Thermostatic shower faucets are known for this problem.
Normally they are the only valves with direct connection between the cold and warm water tubing.
In contrast to non-thermostatic valves, these shower valves mix the water upstream of the flow control valve.
A kitchen valve mixes the water downstream of the open/close valve.
If the trim of the thermostatic faucet is removed, most likely access is possible to the 2 built-in backflow preventer and to the 2 separate built-in shut -off valves (e.g., a Grohe thermostatic shower valve has normally 3 valves).
In this case here, at least 1 of the back flow preventers inside the shower faucet is defect. This could be confirmed by closing the built-in shut-off valve(s).
If another valve (non-thermostatic) in the kitchen is opened for the hottest possible water, i.e. only the warm water side is opened, there will be a huge pressure difference between this open hence low pressure warm water side and the non-opened cold water side, which is under higher pressure.
If the back flow preventer in the thermostatic shower valve is failing, cold water will flow to the warm water tubing.